On Tue, Jul 28, 2015 at 12:36 PM, Luis Ressel <[email protected]> wrote:
> I agree with ais523's interpretation that the the minimum of four and
> none is four; mathematically, this seems to make sense: If we assume
> {'none'} = {} and "minimum of a and b := min {a,b}", then "minimum of
> none and four" evaluates to min {'none',4} = min {4} = 4.
I disagree. The sets {'none'} and {} cannot be the same, because
{'none'} contains the element 'none' and {} does not. Interpreting
'none' as a magical value-that-doesn't-count-as-an-element is
confusing and unnecessary.
Now, I think it's not obvious how to interpret the phrase "adoption
index"—what, exactly, is "the adoption index" of an object?
The obvious answer is that "the adoption index" is the value of the
object's "adoption index" switch. However, this cannot be the correct
answer, because several rules (including Rule 1950 "Decisions with
Adoption Indices", which *defines* the "adoption index" switch) refer
to the property of an object "having an adoption index". Every
proposal or decision has a value for its "adoption index" switch, so
if "the adoption index" meant "the value of the 'adoption index'
switch", all of these references would be pointless. Therefore, I
think the only reasonable definition of "the adoption index" is "the
value of the object's 'adoption index' switch, if this value is an
integer (otherwise, the object has no adoption index)".
So the question is, how should we interpret the phrase "its power is
set to the minimum of four and its adoption index", when "it" has no
adoption index? I think the most straightforward answer is that since
"its adoption index" is meaningless, the whole phrase is meaningless
and has no effect. But that may not be the best answer.
This is a contrived example, but if a rule said something like "a
Periwinkle Ribbon is awarded to the player whose First Proposal Length
is least, where a player's First Proposal Length is the number of
words in the first proposal e ever submitted", presumably any player
who has never submitted a proposal would simply be excluded. Likewise,
the best interpretation of "the minimum of four and its adoption
index", where "it" has no adoption index, may simply be the minimum of
those options which *are* meaningful, the only one of which is four.
In mathematical terms, we're not taking the minimum of the set
{'none', 4}, but rather the minimum of the set {x | either x is 4, or
x is the proposal's adoption index}. When a proposal has no adoption
index, I would say that the sentence "x is the proposal's adoption
index" is meaningful, but false for all values of x, and so the set we
are taking the minimum of is {4}.
—the Warrigal
